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MIT OpenCourseWareMIT 18.02SC Multivariable Calculus, Fall 2010 (2010)

something has gone horribly wrong 8-p
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Instructor: Christine Breiner, David Jordan, Joel Lewis

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

View the complete course: http://ocw.mit.edu/18-02SCF10


This movie is part of the collection: MIT OpenCourseWare

Producer: MIT OpenCourseWare
Audio/Visual: sound, color
Language: English
Keywords: multivariable calculus, vectors, matrices, partial derivatives, double integrals, line integrals, triple integrals, surface integrals

Creative Commons license: Attribution-Noncommercial-Share Alike 3.0


Individual Files

Movie Files MPEG4 Ogg Video 512Kb MPEG4
Coordinate free proofs: centroid of a triangle 24.6 MB
49.9 MB
47.7 MB
Dot products and angles 19.3 MB
39.5 MB
37.2 MB
Components of a vector 11.2 MB
22.7 MB
21.7 MB
Area of a parallelogram 7.5 MB
13.3 MB
14.5 MB
Determinants 10.3 MB
18.9 MB
20.0 MB
Volume of a parallelepiped 6.4 MB
10.7 MB
12.5 MB
Finding area using cross products 11.1 MB
19.4 MB
21.6 MB
Matrix multiplication practice 23.4 MB
38.8 MB
45.3 MB
Solve a linear system using matrices 39.5 MB
68.2 MB
76.9 MB
Equations of planes 30.2 MB
62.2 MB
58.8 MB
Distance of a point to a plane 18.2 MB
37.1 MB
35.1 MB
Systems of linear equations 26.3 MB
54.2 MB
51.0 MB
Parametrized lines and intersections 18.7 MB
36.1 MB
36.4 MB
Parametric line intersecting a plane 17.7 MB
34.6 MB
34.4 MB
Differentiating a vector valued function 31.0 MB
55.3 MB
59.8 MB
Parametric curves: velocity, acceleration, length 18.2 MB
36.0 MB
35.4 MB
Graphing surfaces 17.2 MB
31.2 MB
33.4 MB
Level curves 22.9 MB
44.8 MB
44.3 MB
Level curves and critical points 18.4 MB
35.6 MB
35.7 MB
Partial derivatives 11.7 MB
22.5 MB
22.6 MB
Tangent plane approximation 15.2 MB
26.2 MB
29.4 MB
Least squares 19.9 MB
35.3 MB
38.5 MB
Second derivative test 18.9 MB
37.8 MB
36.8 MB
Max/Min 30.6 MB
60.4 MB
59.5 MB
Total differentials and the chain rule 25.5 MB
46.0 MB
49.2 MB
Tangent planes 19.8 MB
40.3 MB
38.4 MB
Gradient and directional derivative 29.7 MB
59.4 MB
57.7 MB
Lagrange multipliers 22.5 MB
43.7 MB
43.6 MB
Lagrange multipliers (3 variables) 29.0 MB
56.5 MB
56.4 MB
The chain rule with constraints 33.8 MB
62.4 MB
65.0 MB
Gradients - composition 22.5 MB
38.6 MB
43.9 MB
Regions of integration 39.0 MB
75.3 MB
75.7 MB
Changing the order of integration 13.2 MB
25.9 MB
25.8 MB
Integration in polar coordinates 38.2 MB
64.4 MB
74.8 MB
Integrals with density 33.9 MB
59.3 MB
66.2 MB
Change of variables 20.4 MB
36.0 MB
39.2 MB
Integral of exp(-x^2) 20.9 MB
34.5 MB
40.7 MB
Change of variables 43.7 MB
76.6 MB
84.7 MB
Line integrals: path dependence 34.3 MB
62.2 MB
66.1 MB
Line integrals: parametrization independence 27.4 MB
54.0 MB
53.3 MB
Line integrals by geometric reasoning 23.3 MB
47.7 MB
44.9 MB
Fundamental theorem of line integrals 24.3 MB
47.9 MB
47.3 MB
Non-conservative vector fields 21.8 MB
42.2 MB
42.5 MB
Potentials of gradient fields 24.9 MB
43.2 MB
48.3 MB
Green's Theorem: an off center circle 16.4 MB
30.7 MB
31.9 MB
Green's Theorem: area under an arch 18.8 MB
34.5 MB
36.3 MB
Application of Green's theorem 15.8 MB
27.7 MB
30.6 MB
Flux across a curve 31.6 MB
58.4 MB
61.3 MB
Green's Theorem in normal form 24.2 MB
48.1 MB
46.9 MB
Extended Green's Theorem 50.8 MB
99.8 MB
99.2 MB
Domains of vector fields 30.1 MB
52.6 MB
58.2 MB
Volume in cylindrical coordinates 39.8 MB
76.8 MB
77.0 MB
Average height 31.9 MB
66.8 MB
62.2 MB
Moment of inertia of a cylinder 21.8 MB
45.2 MB
42.4 MB
Average distance on a sphere 28.4 MB
54.5 MB
55.1 MB
Gravity and a half-sphere 24.5 MB
47.5 MB
47.8 MB
Flux through easy surfaces 15.0 MB
26.1 MB
28.8 MB
Flux through a square 21.9 MB
36.9 MB
42.6 MB
Flux through surfaces 24.7 MB
46.7 MB
48.2 MB
Flux 24.7 MB
48.9 MB
48.0 MB
Flux and the divergence theorem 26.1 MB
51.9 MB
50.9 MB
Extended Gauss' Theorem 41.4 MB
84.6 MB
80.4 MB
Del and the product rule 18.6 MB
35.6 MB
36.0 MB
Line integral on a helix 24.5 MB
48.7 MB
47.8 MB
Conservative fields and exact differentials 32.3 MB
64.7 MB
63.2 MB
Stokes' Theorem 38.5 MB
78.9 MB
74.7 MB
Extended Stokes' Theorem 34.5 MB
70.5 MB
66.5 MB
Simply connected regions 32.3 MB
62.4 MB
62.9 MB
More Stokes' Theorem 18.3 MB
37.2 MB
35.4 MB
Consequences of Stokes' Theorem 24.3 MB
50.2 MB
47.8 MB
Image Files Thumbnail Animated GIF
Coordinate free proofs: centroid of a triangle 3.3 KB
273.9 KB
Dot products and angles 4.0 KB
217.5 KB
Components of a vector 3.4 KB
128.5 KB
Area of a parallelogram 3.5 KB
79.9 KB
Determinants 3.9 KB
112.9 KB
Volume of a parallelepiped 3.9 KB
67.2 KB
Finding area using cross products 3.9 KB
129.1 KB
Matrix multiplication practice 2.8 KB
246.0 KB
Solve a linear system using matrices 3.1 KB
211.9 KB
Equations of planes 3.5 KB
326.7 KB
Distance of a point to a plane 3.2 KB
195.7 KB
Systems of linear equations 3.8 KB
306.5 KB
Parametrized lines and intersections 3.1 KB
205.9 KB
Parametric line intersecting a plane 3.4 KB
194.3 KB
Differentiating a vector valued function 3.7 KB
326.9 KB
Parametric curves: velocity, acceleration, length 3.1 KB
195.5 KB
Graphing surfaces 2.8 KB
191.5 KB
Level curves 3.4 KB
246.1 KB
Level curves and critical points 3.4 KB
202.3 KB
Partial derivatives 2.9 KB
121.7 KB
Tangent plane approximation 3.6 KB
154.0 KB
Least squares 3.6 KB
220.5 KB
Second derivative test 3.1 KB
207.7 KB
Max/Min 3.1 KB
336.8 KB
Total differentials and the chain rule 3.2 KB
265.2 KB
Tangent planes 3.2 KB
218.6 KB
Gradient and directional derivative 3.4 KB
326.4 KB
Lagrange multipliers 3.6 KB
254.7 KB
Lagrange multipliers (3 variables) 3.2 KB
328.5 KB
The chain rule with constraints 3.2 KB
175.4 KB
Gradients - composition 3.5 KB
233.0 KB
Regions of integration 3.3 KB
219.9 KB
Changing the order of integration 2.6 KB
141.6 KB
Integration in polar coordinates 2.8 KB
194.2 KB
Integrals with density 3.4 KB
176.9 KB
Change of variables 3.6 KB
224.8 KB
Integral of exp(-x^2) 2.9 KB
223.6 KB
Change of variables 2.8 KB
229.6 KB
Line integrals: path dependence 3.2 KB
177.9 KB
Line integrals: parametrization independence 3.4 KB
298.3 KB
Line integrals by geometric reasoning 4.0 KB
258.7 KB
Fundamental theorem of line integrals 3.8 KB
269.3 KB
Non-conservative vector fields 3.5 KB
236.0 KB
Potentials of gradient fields 3.1 KB
246.3 KB
Green's Theorem: an off center circle 3.1 KB
178.2 KB
Green's Theorem: area under an arch 4.0 KB
198.1 KB
Application of Green's theorem 3.6 KB
163.8 KB
Flux across a curve 4.5 KB
329.2 KB
Green's Theorem in normal form 3.8 KB
272.0 KB
Extended Green's Theorem 3.7 KB
267.9 KB
Domains of vector fields 3.0 KB
321.2 KB
Volume in cylindrical coordinates 3.2 KB
216.0 KB
Average height 4.0 KB
362.8 KB
Moment of inertia of a cylinder 3.8 KB
250.5 KB
Average distance on a sphere 4.6 KB
326.7 KB
Gravity and a half-sphere 3.0 KB
248.5 KB
Flux through easy surfaces 3.6 KB
154.6 KB
Flux through a square 3.2 KB
232.1 KB
Flux through surfaces 4.5 KB
263.4 KB
Flux 3.8 KB
264.5 KB
Flux and the divergence theorem 3.6 KB
293.0 KB
Extended Gauss' Theorem 3.1 KB
228.8 KB
Del and the product rule 3.5 KB
204.0 KB
Line integral on a helix 3.0 KB
244.9 KB
Conservative fields and exact differentials 3.5 KB
333.8 KB
Stokes' Theorem 3.5 KB
206.3 KB
Extended Stokes' Theorem 3.5 KB
183.4 KB
Simply connected regions 2.9 KB
320.4 KB
More Stokes' Theorem 3.6 KB
197.8 KB
Consequences of Stokes' Theorem 4.0 KB
263.6 KB
Information FormatSize
MIT18_02SCF10_files.xml Metadata [file]
MIT18_02SCF10_meta.xml Metadata 1.3 KB

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